E-Books →Riemannian Foliations

Free Download Riemannian Foliations by Pierre Molino
English | PDF | 1988 | 348 Pages | ISBN : 1468486721 | 28.9 MB
Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,----,- - . - - p = n - q. The first global image that comes to mind is 1----;- - - - - - that of a stack of "plaques". 1-----;- - - - - - Viewed laterally [transver 1----1- - - - sally], the leaves of such a 1----1 - - - - -. stacking are the points of a 1----1-- --. quotient manifold W of di L..... -' _ mension q. ---~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.